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OneWayAnova (Commons Math 3.2 API)
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org.apache.commons.math3.stat.inference</FONT>
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Class OneWayAnova</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.stat.inference.OneWayAnova</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>OneWayAnova</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
Implements one-way ANOVA (analysis of variance) statistics.

 <p> Tests for differences between two or more categories of univariate data
 (for example, the body mass index of accountants, lawyers, doctors and
 computer programmers).  When two categories are given, this is equivalent to
 the <A HREF="../../../../../../org/apache/commons/math3/stat/inference/TTest.html" title="class in org.apache.commons.math3.stat.inference"><CODE>TTest</CODE></A>.
 </p><p>
 Uses the <A HREF="../../../../../../org/apache/commons/math3/distribution/FDistribution.html" title="class in org.apache.commons.math3.distribution"><CODE>commons-math F Distribution implementation</CODE></A> to estimate exact p-values.</p>
 <p>This implementation is based on a description at
 http://faculty.vassar.edu/lowry/ch13pt1.html</p>
 <pre>
 Abbreviations: bg = between groups,
                wg = within groups,
                ss = sum squared deviations
 </pre>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>1.2</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: OneWayAnova.java 1462423 2013-03-29 07:25:18Z luc $</DD>
</DL>
<HR>

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<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/inference/OneWayAnova.html#OneWayAnova()">OneWayAnova</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default constructor.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/inference/OneWayAnova.html#anovaFValue(java.util.Collection)">anovaFValue</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the ANOVA F-value for a collection of <code>double[]</code>
 arrays.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/inference/OneWayAnova.html#anovaPValue(java.util.Collection)">anovaPValue</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the ANOVA P-value for a collection of <code>double[]</code>
 arrays.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/inference/OneWayAnova.html#anovaPValue(java.util.Collection, boolean)">anovaPValue</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&gt;&nbsp;categoryData,
            boolean&nbsp;allowOneElementData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the ANOVA P-value for a collection of <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/inference/OneWayAnova.html#anovaTest(java.util.Collection, double)">anovaTest</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData,
          double&nbsp;alpha)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Performs an ANOVA test, evaluating the null hypothesis that there
 is no difference among the means of the data categories.</TD>
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<A NAME="OneWayAnova()"><!-- --></A><H3>
OneWayAnova</H3>
<PRE>
public <B>OneWayAnova</B>()</PRE>
<DL>
<DD>Default constructor.
<P>
</DL>

<!-- ============ METHOD DETAIL ========== -->

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<A NAME="anovaFValue(java.util.Collection)"><!-- --></A><H3>
anovaFValue</H3>
<PRE>
public double <B>anovaFValue</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData)
                   throws <A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></PRE>
<DL>
<DD>Computes the ANOVA F-value for a collection of <code>double[]</code>
 arrays.

 <p><strong>Preconditions</strong>: <ul>
 <li>The categoryData <code>Collection</code> must contain
 <code>double[]</code> arrays.</li>
 <li> There must be at least two <code>double[]</code> arrays in the
 <code>categoryData</code> collection and each of these arrays must
 contain at least two values.</li></ul></p><p>
 This implementation computes the F statistic using the definitional
 formula<pre>
   F = msbg/mswg</pre>
 where<pre>
  msbg = between group mean square
  mswg = within group mean square</pre>
 are as defined <a href="http://faculty.vassar.edu/lowry/ch13pt1.html">
 here</a></p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>categoryData</CODE> - <code>Collection</code> of <code>double[]</code>
 arrays each containing data for one category
<DT><B>Returns:</B><DD>Fvalue
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>categoryData</code> is <code>null</code>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the length of the <code>categoryData</code>
 array is less than 2 or a contained <code>double[]</code> array does not have
 at least two values</DL>
</DD>
</DL>
<HR>

<A NAME="anovaPValue(java.util.Collection)"><!-- --></A><H3>
anovaPValue</H3>
<PRE>
public double <B>anovaPValue</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData)
                   throws <A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Computes the ANOVA P-value for a collection of <code>double[]</code>
 arrays.

 <p><strong>Preconditions</strong>: <ul>
 <li>The categoryData <code>Collection</code> must contain
 <code>double[]</code> arrays.</li>
 <li> There must be at least two <code>double[]</code> arrays in the
 <code>categoryData</code> collection and each of these arrays must
 contain at least two values.</li></ul></p><p>
 This implementation uses the
 <A HREF="../../../../../../org/apache/commons/math3/distribution/FDistribution.html" title="class in org.apache.commons.math3.distribution"><CODE>commons-math F Distribution implementation</CODE></A> to estimate the exact
 p-value, using the formula<pre>
   p = 1 - cumulativeProbability(F)</pre>
 where <code>F</code> is the F value and <code>cumulativeProbability</code>
 is the commons-math implementation of the F distribution.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>categoryData</CODE> - <code>Collection</code> of <code>double[]</code>
 arrays each containing data for one category
<DT><B>Returns:</B><DD>Pvalue
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>categoryData</code> is <code>null</code>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the length of the <code>categoryData</code>
 array is less than 2 or a contained <code>double[]</code> array does not have
 at least two values
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the p-value can not be computed due to a convergence error
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the maximum number of iterations is exceeded</DL>
</DD>
</DL>
<HR>

<A NAME="anovaPValue(java.util.Collection, boolean)"><!-- --></A><H3>
anovaPValue</H3>
<PRE>
public double <B>anovaPValue</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;<A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&gt;&nbsp;categoryData,
                          boolean&nbsp;allowOneElementData)
                   throws <A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A>,
                          <A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Computes the ANOVA P-value for a collection of <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A>.

 <p><strong>Preconditions</strong>: <ul>
 <li>The categoryData <code>Collection</code> must contain
 <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A>.</li>
 <li> There must be at least two <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A> in the
 <code>categoryData</code> collection and each of these statistics must
 contain at least two values.</li></ul></p><p>
 This implementation uses the
 <A HREF="../../../../../../org/apache/commons/math3/distribution/FDistribution.html" title="class in org.apache.commons.math3.distribution"><CODE>commons-math F Distribution implementation</CODE></A> to estimate the exact
 p-value, using the formula<pre>
   p = 1 - cumulativeProbability(F)</pre>
 where <code>F</code> is the F value and <code>cumulativeProbability</code>
 is the commons-math implementation of the F distribution.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>categoryData</CODE> - <code>Collection</code> of <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A>
 each containing data for one category<DD><CODE>allowOneElementData</CODE> - if true, allow computation for one catagory
 only or for one data element per category
<DT><B>Returns:</B><DD>Pvalue
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>categoryData</code> is <code>null</code>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the length of the <code>categoryData</code>
 array is less than 2 or a contained <A HREF="../../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A> does not have
 at least two values
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the p-value can not be computed due to a convergence error
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the maximum number of iterations is exceeded<DT><B>Since:</B></DT>
  <DD>3.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="anovaTest(java.util.Collection, double)"><!-- --></A><H3>
anovaTest</H3>
<PRE>
public boolean <B>anovaTest</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</A>&lt;double[]&gt;&nbsp;categoryData,
                         double&nbsp;alpha)
                  throws <A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Performs an ANOVA test, evaluating the null hypothesis that there
 is no difference among the means of the data categories.

 <p><strong>Preconditions</strong>: <ul>
 <li>The categoryData <code>Collection</code> must contain
 <code>double[]</code> arrays.</li>
 <li> There must be at least two <code>double[]</code> arrays in the
 <code>categoryData</code> collection and each of these arrays must
 contain at least two values.</li>
 <li>alpha must be strictly greater than 0 and less than or equal to 0.5.
 </li></ul></p><p>
 This implementation uses the
 <A HREF="../../../../../../org/apache/commons/math3/distribution/FDistribution.html" title="class in org.apache.commons.math3.distribution"><CODE>commons-math F Distribution implementation</CODE></A> to estimate the exact
 p-value, using the formula<pre>
   p = 1 - cumulativeProbability(F)</pre>
 where <code>F</code> is the F value and <code>cumulativeProbability</code>
 is the commons-math implementation of the F distribution.</p>
 <p>True is returned iff the estimated p-value is less than alpha.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>categoryData</CODE> - <code>Collection</code> of <code>double[]</code>
 arrays each containing data for one category<DD><CODE>alpha</CODE> - significance level of the test
<DT><B>Returns:</B><DD>true if the null hypothesis can be rejected with
 confidence 1 - alpha
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>categoryData</code> is <code>null</code>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the length of the <code>categoryData</code>
 array is less than 2 or a contained <code>double[]</code> array does not have
 at least two values
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>alpha</code> is not in the range (0, 0.5]
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the p-value can not be computed due to a convergence error
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the maximum number of iterations is exceeded</DL>
</DD>
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